Confinement in de Sitter Space and the Swampland

TL;DR

This paper explores how the Festina Lente swampland criterion constrains the relationship between confinement scales and the Hubble parameter in holographic de Sitter models, revealing limitations on parameter hierarchies and implications for metastability.

Contribution

It demonstrates how Festina Lente imposes constraints on holographic de Sitter models, especially regarding metastability and parameter hierarchies, using the Karch-Randall setup.

Findings

Festina Lente constrains confinement-Hubble scale relation in holographic models.

Metastable de Sitter minima are near decay, affecting validity.

No contradictions found with swampland conjectures.

Abstract

The relation between confinement scale $\Lambda_c$ of a gauge theory and the Hubble scale $H$ of the background quasi de Sitter space, required to satisfy the Festina Lente criteria ($\Lambda_c \gtrsim H$) from swampland principles, are investigated for a holographic theory using the Karch-Randall setup. A purely gravitational description admits unstable de Sitter extremum, and the requirement of Festina Lente translates into requirements of a perturbative gravitational dual, but prohibits an arbitrarily small hierarchy for other parameters fixed. With an additional scalar sector, the theory admits metastable de Sitter minima, and the requirement of Festina Lente imposes constraints on the parameters. For some range of parameters where Festina Lente could be constraining, the de Sitter minimum is very close to decay, thus invalidating the applicability. Further consequences of the finite lifetime of the dS extrema and the relation with related swampland conjectures are investigated, and no contradictions are found. These results make case for the consistency and utility of the Karch-Randall setup, clarify the implications of Festina Lente for holographic theories, and connect Festina Lente to other swampland conjectures.